Pressure-driven distillation using air-trapping membranes for fast and selective water purification

Membrane technologies that enable the efficient purification of impaired water sources are needed to address growing water scarcity. However, state-of-the-art engineered membranes are constrained by a universal, deleterious trade-off where membranes with high water permeability lack selectivity. Current membranes also poorly remove low–molecular weight neutral solutes and are vulnerable to degradation from oxidants used in water treatment. We report a water desalination technology that uses applied pressure to drive vapor transport through membranes with an entrapped air layer. Since separation occurs due to a gas-liquid phase change, near-complete rejection of dissolved solutes including sodium chloride, boron, urea, and N-nitrosodimethylamine is observed. Membranes fabricated with sub-200-nm-thick air layers showed water permeabilities that exceed those of commercial membranes without sacrificing salt rejection. We also find the air-trapping membranes tolerate exposure to chlorine and ozone oxidants. The results advance our understanding of evaporation behavior and facilitate high-throughput ultraselective separations.


Structure, hydrophobicity, and stability of the fabricated membranes
The structure of the fabricated anodic aluminum oxide (AAO) membranes was analyzed using field emission scanning electron microscopy (FESEM). Pore size and surface porosity of the modified AAO membranes were determined by Image J analysis of FESEM images. Assuming cylindrical pores of AAO membranes, the ratio of nanopore area over the membrane area is considered the membrane porosity. The effective size of the nanopores were considered as the diameter of the circles having the same area as the pore. The equivalent pore size and porosity were then estimated from at least twenty different locations on each sample.

Confirmation of surface modification on AAO membranes
We examined the chemical properties of modified AAO membranes by Fourier transform infrared spectroscopy (FTIR). FTIR spectra showed decreased transmittances at 1171 and 1232 cm -1 corresponding to -CF2 stretching, indicating that hydrophobic fluorosilane (FAS) molecules were present on the AAO membrane surface ( fig. S4). A slight increase in the peak corresponding to hydroxyl groups (-OH) at 3400 cm -1 confirmed that substantial consumption of -OH groups occurred. Energy-dispersive X-ray spectroscopy (EDS) analysis showed changes in the elemental composition of pristine and modified AAO membranes. New characteristic F and Si peaks appear at 0.7 and 1.7 keV in the modified samples, indicating 1.57% and 0.37% wt of F and Si on an atomic basis ( fig. S5A,B). Along with a high water contact angle, EDS and FTIR spectra provide evidence of the effective hydrophobic modification with low-surface energy FAS. Notably, the bonding between silane molecules and AAO substrate is stable under chlorine exposure (1000 ppm in 36 h at pH 5) as there is no substantial difference between FTIR spectra of the chlorine-exposed and the unused hydrophobic AAO membranes ( fig. S4).

Simulating mass and heat flux across membranes
The governing equations for mass flux in the system are provided in the Materials and Methods.
Heat flux transferred across the membrane, q, is the sum of convective and conductive heat transfer: where km is membrane thermal conductivity, δ is membrane thickness, hvap is the enthalpy of vaporization of water (40.65 kJ mol -1 ). Convective heat is the heat of vaporization for water transport from the feed to the permeate. Conductive heat is the heat transport from the permeate back to the feed through the membrane material and air gap.
Temperature polarization due to convective heat transfer leads to a lower temperature at the feedmembrane interface and a higher temperature at the permeate-membrane interface, which reduces the overall vapor pressure difference (34). Temperature polarization was accounted for using the following equations: where hf and hp are the heat transfer coefficients of the feed and permeate boundary layers, respectively, and cl is the specific heat capacity of liquid water.
Concentration polarization accounts for the accumulation of rejected solutes near the feedmembrane interface and decreases the water flux due to an elevated osmotic pressure difference across the membrane. Solute concentration at the membrane-solution interface on the feed side ( ',) ) is given by (24): where kf is the mass transfer coefficient through the feed boundary layer, and Cf,b is the bulk salt concentration in the feed. It should be noted that on the permeate, the solute concentration at the membrane surface, Cp,m, and in the bulk, Cp,b, are considered equal.
Heat and mass transfer coefficients were assumed to be fixed since the variations in h (500-22000 W m -2 K -1 ) and k (0.02-0.04 kg m -2 s -1 ) result in less than 5% changes in the water flux. Thus, our simulations assume hf = hp = 1000 W m -2 K -1 and kf = 0.0278 kg m -2 s -1 .
The vapor permeability coefficient of water (Bw) was determined via the evaporation rate of water obtained from the Hertz hypothesis and total transport resistance (24): where is the membrane porosity, Mw is the molecular weight of water, Rg is the universal gas constant, Rt is the transmission resistance, and Ri,f and Ri,p are the interfacial resistances at the liquidvapor interfaces of the feed and permeate, respectively .
Transmission and interfacial resistances can be calculated by the following equations (24): where p0(T) is the vapor pressure of water at temperature T, pt is the pressure of the gas mixture in the membrane pores, vw is the mean molecular speed of water vapor, Dwa is the diffusion coefficient of water in air, η is the transmission probability, and σ(T, P) is the condensation coefficient of water (also referred to as the mass accommodation coefficient of water).
Transmission probability in cylindrical nanopores can be calculated using Berman's formula (54): where L = δ/a is the pore aspect ratio.
We solved the non-linear system of equations to simulate transmembrane mass and heat flux accounting for the impacts of temperature and concentration polarization. The models above have been widely used for vapor transport in related membrane processes (e.g., membrane distillation, osmotic distillation) with a high degree of accuracy (19,51).

Determination of membrane pore wetting pressure and theoretical minimum thickness
Pore wetting should be avoided to maintain the air gap that enables selectivity in the fabricated membranes. To resist wetting from an applied hydraulic pressure, membranes should have a small pore radius and high hydrophobicity as described by the Young-Laplace equation (22,34): where β is a pore geometry factor, CS is the surface tension of the liquid-vapor interface, T+ is the equilibrium water contact angle, r is the pore radius, and ΔPmax is the maximum hydraulic pressure difference across the membrane meniscus prior to wetting, also known as the liquid entry pressure To prevent pore wetting, the pore length must also be long enough to prohibit wetting of the pore from being thermodynamically favorable. Assuming the membrane has cylindrical pores, a tortuosity of 1, and a pore length equal to membrane thickness, the critical aspect ratio to prevent pore wetting can be defined as follows (24): where δ is the membrane thickness, r is the pore radius, is the geometric angle between the pore axis and a tangential line to the liquid-vapor interface. For a given hydraulic pressure difference, we calculate the geometric contact angles as follows: (S11) where )#O is the maximum pore radius corresponding to the intrinsic contact angle T+ (assumed to be 120º).
Equation S10 always results in a smaller pore size than Equation S9 given a finite membrane thickness, therefore it is the more conservative constraint for pore wetting. Minimum thicknesses for relevant ranges of pore sizes and applied pressures are shown in fig. S6B. Using an applied pressure of 6.89 bar and a pore size of 75.5 nm, the membrane thickness should be at least 116 nm to maintain the air gap and avoid wetting. All fabricated membranes presented in this work have hydrophobic layer thicknesses above this threshold. Membrane fabricated with thicknesses below this threshold showed wetting, as predicted from theory.

Accounting for effect of concentration polarization
Concentration polarization was accounted for in measurements by measuring both the pure DI water flux (Jw,DI) and the water flux with 50 mM NaCl (Jw,NaCl) at the same applied pressure difference, ∆P. These measurements were used with the water flux equations in both scenarios (55): where Lp is the water permeability coefficient of the membrane and Δπm is the osmotic pressure difference between the feed-membrane and permeate-membrane interfaces. From the above equations, Δπm can be calculated as follows: The salt concentration at feed-membrane interface (Cf,m) was then estimated using the Van't Hoff equation (36): where ν is the Van't Hoff coefficient, ϕ is the osmotic coefficient, and M is the molar mass of water.
For a monovalent salt such as NaCl, the Van't Hoff coefficient is 2. Note that the above equation assumes that the concentration in the permeate does not contribute substantially to the osmotic pressure difference as the membranes are highly selective for solutes tested in this work. The concentration polarization factor is defined as the ratio of the concentration at the feed-membrane interface (Cf,m) and the bulk feed concentration (Cf,b): The apparent salt rejection (Rapp) and true salt rejection (Rtrue) are calculated as follows: where Cp is the permeate concentration.

Performance testing of commercial thin-film composite reverse osmosis membranes
The performance of the fabricated air-trapping membranes was compared to that of thin-film composite (TFC) polyamide RO membranes: SW30-XLE, NF90, and NF270 (Dupont, DE, USA).
Polyamide RO membranes were stored in a cold dark room at a temperature of 4 °C to prevent any degradation. To obtain the permeability-selectivity trade-off, SW30-XLE membranes were chlorinated at pH 7 using different chlorine concentrations ranging from 100 to 10000 ppm for 1 h as described in the literature and compared to curves determined in prior work (56,57).

Agreement between water vapor flux and predictions from the Dusty-Gas Model
Using the average pore size determined from FESEM images, experimental water fluxes of the fabricated AAO membranes can be compared to simulated values using the Dusty-Gas Model (Equations 1-7 and S1-S8). In modeling the water flux of membranes, several assumptions were made regarding membrane properties. Thermal conductivity of AAO membranes was determined using an existing empirical equation (58): where km is the thermal conductivity of the membrane (W m -1 K -1 ) and ε is the membrane porosity (46). The AAO membranes have straight cylindrical pores, and their tortuosity, τ, was approximated to equal 1.
The average pore sizes and porosities of the three AAO membranes tested are estimated as 75.5,

Long-term desalination by fabricated AAO membranes
We examined the desalination performance of the uniformly coated AAO membranes with a pore

Liquid entry pressure and transport in wetted membranes
We gradually increased the transmembrane pressure difference, and continually monitored water flux and salt rejection. There was a threshold pressure, called the liquid entry pressure (LEP), where water transport transitioned from a salt rejecting desalination regime with nonwetted pores to a non-salt rejecting regime with wetted pores. The liquid entry pressures (LEPs) for 20, 40, and 80 nm pore size membranes were 48.3, 31.0, and 13.8 bar, respectively, in agreement with Young-Laplace predictions for an intrinsic contact angle of 120° (Equation S9). When the hydraulic pressure on the feed exceeded the liquid entry pressure, membrane wetting occurred and was irreversible as subsequent decreases in hydraulic pressure showed non-selective liquid water transport in the wetted regime.
We studied liquid flow through wetted pores to validate that membrane pores were not clogged during modification. Liquid flow through the pores in the wetted regime was four orders of magnitude higher than vapor transport in desalination regime when the pores were not wetted ( fig.   S9). Liquid water flux is consistent with laminar liquid flow through a cylindrical pore modeled using the Hagen-Poiseuille equation (59): where dp is the membrane pore diameter, ε is the membrane porosity, ΔP is the transmembrane hydraulic pressure, τ is the membrane tortuosity, ηw is the dynamic viscosity of water (8.89 × 10 -4 Pa s at 25 °C), δ is the membrane thickness, and Jw,l is the liquid water flux through the membrane.

Impact of heat transfer on water vapor transport
Transport of water vapor through the membrane results in heat transfer associated with evaporation and condensation which can negatively impact the membrane flux. We estimated the heat transfer in our experiments and quantified the contribution to flux decline from temperature polarization, a phenomenon that occurs as the liquid-vapor interface on the feed side cools and the interface on the permeate side heats, reducing the partial vapor pressure difference that drives water vapor through the membrane. The impact of temperature polarization can be estimated by balancing heat transfer from the latent heat of vaporization, which is known from the water flux, and conductive heat transfer through the thin air gap (Equation S2, S3). For the ultrathin membranes used in this study, it was found that temperature polarization resulted in a negligible temperature difference across the membrane (less than 1 × 10 -3 °C), which would have less than a 2.5% decrease in the water flux.
Negative impacts from heat transfer across the membrane were thus concluded to be negligible for our system since the ultrathin membranes had an extremely high thermal conductivity that prevented any substantial buildup of temperature. We note that the experimental measurement of the temperature difference across the membrane as not possible due to the extremely low difference in temperature.
To draw more general conclusions on the effect of heat transfer in the process, simulations of heat transfer were conducted for small membrane elements and large-scale membrane modules.
Membranes with different representative thicknesses and thermal conductivities were simulated using the Dusty-Gas Model accounting for the latent heat of evaporation/condensation and conductive heat transfer across the membrane (Equations 1-7 and S1-S8). The flux decline due to temperature polarization was generally less than 10% in membranes with thicknesses varying from 0.1 to 1 µm that had a high thermal conductivity comparable to the alumina membranes (1.0 W m -1 K -1 ). We observed a maximum temperature difference of 2.7 × 10 -3 °C at a thickness of 30 µm ( fig.   S10B, C). Water flux decline due to temperature polarization was as high as 16% for 10 µm thick membranes with a lower thermal conductivity comparable to hydrophobic polymeric membranes (0.1 W m -1 K -1 ), which corresponded to a maximum temperature difference of 0.021 °C. The relatively low effect of temperature polarization on water flux is attributed to conductive heat transfer from the permeate to the feed, which prevents a substantial temperature difference from forming across the membrane ( fig. S10A).
Experimental measurements supported the minor effect of heat transfer on the water flux.
Specifically, measurements of DI water flux through all membranes showed a near linear increase in water flux as a function of the applied pressure ( Fig. 2A). If substantial temperature polarization was occurring, we would expect that water flux would have a nonlinear relationship with hydraulic pressure, where high water fluxes at high pressures would lead to substantial convective heat transfer that would limit the achievable water flux.

Module-scale modeling of water vapor transport
Bulk temperature changes in large-scale membrane modules due to heat transfer across the membranes were simulated using the finite-difference method. We modeled a membrane module with co-current flow, which is an approximation of the behavior in a pressurized membrane module.
The differential equations for mass and heat transfer were discretized using the finite difference method to obtain the heat flux, flow rates, and concentrations along the module: where

Simulating module-scale changes in bulk temperature due to heat transfer
We conducted simulations to explore whether heat transfer through the membrane via the enthalpy of vaporization could lead to large-scale changes in the bulk feed and permeate solution temperatures. Water and heat fluxes over the entire module length were used to obtain bulk temperatures in a variety of operating conditions and membrane properties ( fig. S11A). In fig.   S11C, the x-axis is the relative position in the simulated membrane module, and the y-axis is the bulk temperature difference between the feed and permeate sides. Four realistic representative values of membrane thickness and thermal conductivity were used for the model. Simulations for membrane modules with a 50% recovery showed that, for any realistic range of membrane properties, the water flux losses due to bulk temperature changes were less than 2.8% ( fig. S11B).
The temperature difference was minimal with the thermal conductivity of 1.0 W m -1 K -1 . When the thermal conductivity was 0.1 W m -1 K -1 , the maximum temperature difference was about 0.018 K.
Thus, heat transfer across the membrane will result in minor losses in water flux and negligible changes in bulk temperature difference in pressure-driven distillation since heat conduction through the membrane and air gaps alleviate the detrimental effects of latent heat transfer.

Rejection of boron, urea, and N-nitrosodimethylamine
Boron rejection was tested using a feed concentration of 5 mg/L which is close to that in real seawater (60). Boron concentrations of feed and permeate samples were quantified using inductively coupled plasma mass spectroscopy (Agilent 7700x, CA, USA). The detection limit of the instrument is 0.241 µg/L, allowing precise determination of boron rejection even when it is close to 99%. Urea concentrations were analyzed via absorbance at the wavelength of 520 nm. As shown in fig.   S13A and S13B, two distinct regions of absorbance were found that correspond to two concentration ranges: 0.001-0.3 mM (purple complex) and greater than 0.3 mM (orange complex).
The absorbance increases with urea concentration in the concentration range from 0.001 to 0.3 mM but decreases with urea concentration at concentrations greater than 0.3 mM.
Rejection of NDMA was measured with an initial concentration of 100 mg/L, a temperature of 25 °C and an applied pressure of 10.3 bar. The high feed concentration was used to allow a detection limit of at least 99.9% rejection. NDMA concentration was immediately measured after the rejection tests using a high-performance liquid chromatograph (HPLC) (Agilent 1220, CO, USA) equipped with a UV-Vis detector and a 5 μm particle size reverse phase column (Agilent Eclipse Plus C-18, CO, USA) (50). The mobile phase was 10/90 (v/v) methanol/ultrapure water running at a flow rate of 1 mL/min. The wavelength of NDMA detection is 228 nm. Each sample was injected twice to confirm the NDMA measurement was accurate. The retention time and injection volume were 2.6 min and 100 µL, respectively. A calibration curve was built to determine NDMA concentration of the feed and permeate waters within the range of 0.1 to 5000 µM ( fig. S13C).

Exposure of the membranes to chemical oxidants
The oxidation tolerance of fabricated AAO and commercial polyamide membranes were examined by submerging in chlorine and ozone solutions at a certain concentration and pH inside a beaker fully covered by aluminum foil to prevent any photodegradation. 1000 ppm chlorine solution was prepared daily and 25 ppm ozone solution was continuously produced from an ozone generator. pH of chlorine and ozone solutions was adjusted using 0.1 M HCl and 0.1 M NaOH. Chlorine and ozone concentrations were monitored throughout the experiment to ensure the membranes were exposed to consistent doses of the oxidants (fig. S14).
Total chlorine concentration was measured by a handheld colorimeter and chlorine test kit (Hach DR300, CO, USA). Since the detection range of this meter is 0.02-2 mg/L, collected chlorine samples were diluted 500 times before measurement. A powder pillow containing N,N-diethyl-pphenylenediamine was mixed with 10 mL of diluted sample. The mixture was slowly swirled for 20 s to form a pink complex.
Ozone concentration was measured via UV-Vis absorbance at the wavelength of 258 nm (51).
A 1 cm quartz cuvette was employed, and DI water was used as the baseline for UV-Vis measurements. For each measurement, 1 mL of ozone solution was immediately taken from the reactor, transferred to a clean cuvette, and the corresponding absorbance was measured. The entire procedure was carried out in less than 5 s to prevent loss of ozone due to evaporation.           Transport mechanism and resistances Solution-diffusion transport through polymer matrix (7) Vapor transport in Knudsen and molecular diffusion regimes (61) Vapor transport in Knudsen diffusion regime. Interfacial resistances from evaporation and condensation are important (36) Ideal membrane properties Thin layer of dense polyamide or cellulose acetate (2) Pore size of 100-1000 nm. Optimal thickness of hydrophobic layer is 50-200 µm (61) Pore size less than 100 nm. Thin hydrophobic layer less than 1 µm Estimated energy efficiency 1-2 kWh m -3 (2) Greater than 7.7 kWh m -3 (19) Similar to RO (*) Oxidation resistance Polyamide membranes tolerate chloramines but degrade from chlorine and ozone (62) Hydrophobic materials generally tolerant to chlorine and ozone (17,41) Hydrophobic materials generally tolerant to chlorine and ozone (17,41) Selectivity Governed mostly by size, charge, and dielectric constant of the solutes (63)